TY - JOUR

T1 - Post-Newtonian Hamiltonian description of an atom in a weak gravitational field

AU - Schwartz, Philip K.

AU - Giulini, Domenico

N1 - Funding Information: We thank Klemens Hammerer for pointing out Ref. [1] and asking questions that initiated and encouraged the work reported here, as well as for critical reading of the manuscript and the suggestion of improvements. We are grateful to Alexander Friedrich for pointing out Ref. [9] to us. This work was supported by the Deutsche Forschungsgemeinschaft through the Collaborative Research Centre 1227 (DQ-mat), project B08. We thank all members for fruitful and encouraging discussions on topics related to the one dealt with in this paper.

PY - 2019/11

Y1 - 2019/11

N2 - We extend the systematic calculation of an approximately relativistic Hamiltonian for center of mass and internal dynamics of an electromagnetically bound two-particle system by Sonnleitner and Barnett [Phys. Rev. A 98, 042106 (2018)10.1103/PhysRevA.98.042106] to the case including a weak post-Newtonian gravitational background field, described by the Eddington-Robertson parametrized post-Newtonian metric. Starting from a proper relativistic description of the situation, this approach allows us to systematically derive the coupling of the model system to gravity, instead of "guessing" it by means of classical notions of relativistic effects. We embed this technical result into a critical discussion concerning the problem of implementing and interpreting general couplings to the gravitational field and the connected problem of how to properly address the question concerning the validity of the Equivalence Principle in Quantum Mechanics.

AB - We extend the systematic calculation of an approximately relativistic Hamiltonian for center of mass and internal dynamics of an electromagnetically bound two-particle system by Sonnleitner and Barnett [Phys. Rev. A 98, 042106 (2018)10.1103/PhysRevA.98.042106] to the case including a weak post-Newtonian gravitational background field, described by the Eddington-Robertson parametrized post-Newtonian metric. Starting from a proper relativistic description of the situation, this approach allows us to systematically derive the coupling of the model system to gravity, instead of "guessing" it by means of classical notions of relativistic effects. We embed this technical result into a critical discussion concerning the problem of implementing and interpreting general couplings to the gravitational field and the connected problem of how to properly address the question concerning the validity of the Equivalence Principle in Quantum Mechanics.

UR - http://www.scopus.com/inward/record.url?scp=85075613801&partnerID=8YFLogxK

U2 - 10.48550/arXiv.1908.06929

DO - 10.48550/arXiv.1908.06929

M3 - Article

AN - SCOPUS:85075613801

VL - 100

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 5

M1 - 052116

ER -